Basic Microeconomics / Calculus Question

[shawny boy]

U(f,s) = f * s

U(f,s) = f^.5 * s^.5

U(f,s) = ln(f) + ln(s)

What is the marginal rate of substitution MRSfs?

Okay, so I think we want to find the slope of the function at the point that maximizes utility, so do I just take the first derivative of each function? I'm not given a budget line or any information about the relative costs of these two substitutes. I'm a little lost. Thanks in advance for any pointers (or preferably detailed explanations with math and theory)

Shawn

[Sephus]

MRSfs = MUf/MUs

MUf = dU/df
MUs = dU/ds

so you find the partial derivative with respect to f and divide it by the partial derivative with respect to s.

in the first case for U(f,s) = f * s, dU/df = s, and dU/ds = f, so MRSfs = s/f.

what you've found is the opposite of the slope of the indifference curve that goes through the point (f,s). so on the U=1 curve, at point (1,1) the slope is -(1/1).